Question

Ramon wants to make an acute triangle with three pieces of wood. So far, he has cut wood lengths of 7 inches and 3 inches. He still needs to cut the longest side. What length must the longest side be in order for the triangle to be acute?

a) exactly inches

b) greater than inches but less than 10 inches

c) less than inches but greater than 7 inches

d) not enough information given

Answer 1

Answer: c

Explanation:

Answer 2

Option c - less than
`√(58)` inches but greater than 7 inches.

Explanation:

Given : Ramon wants to make an acute triangle with three pieces of wood. So far, he has cut wood lengths of 7 inches and 3 inches.

To find : What length must the longest side be in order for the triangle to be acute?

Solution :

According to property of triangle,

If the square of larger side of triangle is equating to the sum of square of smaller side

If
`a^2<b^2+c^2` the triangle is acute triangle

where, a is the larger side and b,c are the smaller side

According to question, Let a=a , b=7, c=3

`a^2<7^2+3^2`

`a^2<49+9`

`a<√(58)`

Means to be a acute triangle third side must be less than
`√(58)` inches but greater than 7 inches.

Therefore, Option c is correct.