# Question #1b82b

##### 2 Answers

Tina would need a **minimum** of

#### Explanation:

The two triangles are

Then, by the properties of similar triangles:

Since side

**So #DG = 3*7#in #= 21#in.**

Perimeter of #DFG = 15+18+21 = 54in.

This is the correct answer and a correct method for the solution.

There is also a method of solving the larger triangle with a formula to find the value of the common angle using the three given sides of the smaller triangle:

By the way that angle is

Then we can apply the same formula to the larger triangle:

Answer checked!

#### Explanation:

When we see the triangles, we can say that the triangles are similar to each other. The corresponding sides are in multiples of their common sides.

We can say that,

#color(orange)("AB"xx3="DF"#

#color(orange)("BC"xx3="FG"#

So,

#color(orange)("DG"=7xx3=21#

Now we know the three sides of the triangle.We can find the area of the triangle using the Heron's formula

#color(blue)("Area"=sqrt(s(s-a)(s-b)(s-c))#

Where,

#color(blue)(s=(15+18+21)/2=27#

Let's apply the values to the formula

Split into prime factors

So, the minimum area of wood required is

Hope this helps...! :)