Practice G.6

A childcare center has three square child play areas that border a right triangular office space. Which statement is true?

• The value of x must be 14 because 2(5) + x = 2(12), so x = 14.

• The value of x must be 17 because 5 + 12 = x, so x = 17.

• The value of x must be 34 because 2(5) + 2(12) = x, or 10 + 24 = x, so x = 34.

The diagram shows three squares that are joined at vertices to form a right triangle, where the area of Square L is 576 cm² and the area of Square M is 49 cm². Which statement is true?

• A. The area of Square N is less than the difference of the areas of Square L and Square M.

• B. The area of Square N is greater than the sum of the areas of Square L and Square M.

• C. The area of Square N is equal to the sum of the areas of Square L and Square M.

• D. The area of Square N is equal to the difference of the areas of Square L and Square M.

A landscaper builds a triangular garden with side lengths of a feet, b feet, and c feet, where c is the greater than both a and b. Which statement is true?

• The triangle will be a right triangle if c is equal to (2a - 2b) feet

• The triangle will be a right triangle if c is equal to (2a + 2b) feet

Right triangle PQR is formed by arranging three squares along its sides, as shown. Which statement must be true if angle PQR is a right angle?

• A. The sum of the areas of squares X and Z is equal to the area of square Y.

• B. The sum of the areas of squares Y and Z is equal to the area of square X.

• C. The sum of the perimeters of squares X and Z is equal to the perimeter of square Y.

• D. The sum of the perimeters of squares Y and Z is equal to the perimeter of square X.

Consider the figure. If a student draws a grid in the empty box to prove the triangle is a right triangle, which statement is true?

• The dimensions of the grid should be 7 by 7 because 25 + 144 = (7 ⋅ 7).

• The dimensions of the grid should be 12 by 5 because 25 + 144 = (12 ⋅ 5).

• The dimensions of the grid should be 13 by 13 because 25 + 144 = (13 ⋅ 13).

• The dimensions of the grid should be 17 by 17 because 25 + 144 = (17 ⋅ 17).

Squares 1, 2, and 3 are joined at different vertices, creating a right triangle. Which could represent the areas of squares 1, 2, and 3?

• square 1 = 30 square units; square 2 = 36 square units; square 3 = 42 square units

• square 1 = 30 square units; square 2 = 72 square units; square 3 = 78 square units

• square 1 = 50 square units; square 2 = 100 square units; square 3 = 200 square units

• square 1 = 50 square units; square 2 = 150 square units; square 3 = 200 square units

Consider the right triangle, where two sides are each bordered by a box filled with squares having side lengths of 1 unit. If the empty box is filled using the same squares, what will the dimensions of the empty box be?

• 6 units by 8 units

• 8 units by 10 units

• 10 units by 10 units

• 14 units by 14 units

Tonya used side lengths a, b, and c to make different triangles. When Tonya only changed the length of side c, she noticed patterns with the side lengths used and the types of triangles formed. Which statement is true from Tonya's investigation?

• If the length of side c is equal to 2a-2b, the triangle formed is a right triangle.

• If the length of c is equal to 2a+2b, the triangle formed is a right triangle.

Which are the dimensions of a right triangle?

• 12cm, 35cm, 37cm

• 10cm, 15cm, 20cm

• 8cm, 12cm, 16cm

• 3cm, 4cm, 7cm

If triangle abc is a right triangle, which statement must be true?

• The sum of the areas of squares B and C is equal to the area of square A

• The sum of the perimeters of squares A and B is equal to the perimeter of square C.

• The sum of the areas of squares A and B is equal to the area of square C

• The sum of the perimeters of B and C is equal to the perimeter of square A