Question

A carpenter added a diagonal brace to gate. The gate is 8ft. Wide and 10 ft. Tall. How long is the brace

Answer 1

The brace is
`2√(41)` ft ≅ 12.806 ft long

Explanation:

The length of the diagonal of a rectangle can be found using this rule

`d=\sqrt{l^(2)+w^(2)}` , where

• l is its length

• w is its width

∵ The gate has shaped a rectangle

∵ Its length = 10 ft

∵ Its width = 8 ft

∴ l = 10 and w = 8

∵ The brace is the diagonal

→ By using the rule above

∴
`d=\sqrt{(10)^(2)+(8)^(2)}=√(100+64)=√(164)`

∴ The length of the brace =
`2√(41)` ≅ 12.806 ft

∴ The brace is
`2√(41)` ≅ 12.806 ft long