Question

Renee is sewing a quilt whose pattern contains right triangles. Each quilt piece has a height of 6 inches. And an area of 24 inches. How long is the base of each quilt piece?

Answer 1

Base of quilt is 8 inch.

Explanation:

Refer to the attachment.

Given that pattern on the quilt is right angle triangle. Consider ΔABC as right angle triangle where ∠ABC=90°.

Given that area of triangle is 24 in² and height is 6 inch that is, AB = 6 inch.

To find the base use formula for area of right angle triangle.

`Area\:of\:triangle=(1)/(2)* base* height`

Substituting the values,

`24=(1)/(2)* base* 6`

Simplifying,

`24=(6)/(2)* base`

Multiplying both sides by
`(2)/(6)`,

`24* (2)/(6)=(6)/(2)* base* (2)/(6)`

Simplifying,

`24* (2)/(6)=base`

Dividing the numbers,

`8=base`

Therefore, length of base of each quilt piece is 8 inch.