Question

Julius built a triangular display case for his coin collection. The height of the display case is six inches less than twice the width of the base. The area of the of the back of the case is 70in2. Find the width and height of the case.

Answer 1

Answer: Width will be 10 inches

and height will be 14 inches.

Explanation:

Since we have given that

The are of the triangular display case is 70 sq. in.

Let the width of the base be x

Let the height of the base be 2x-6

As we know the formula for " Area of triangle " i.e.

$\text{ Area of triangle }=\frac{1}{2}\times b\times h$

According to question,

$70=\frac{1}{2}\times x\times (2x-6)\\\\70\times 2=x(2x-6)\\\\140=2x^2-6x\\\\140=2(x^2-3x)\\\\\frac{140}{2}=x^2-3x\\\\70=x^2-3x\\\\x^2-3x-70=0\\\\x^2-10x+7x-70=0\\\\x(x-10)+7(x-10)=0\\\\(x-10)(x+7)=0\\\\x=10,-7$

Since width can't be negative so, we take width = 10 inches

And height is given by

$2x-6=2\times10-6=20-6=14\ in$

Hence, width will be 10 inches

and height will be 14 inches.