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.
[tex]\text{ Area of triangle }=\frac{1}{2}\times b\times h[/tex]
According to question,
[tex]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[/tex]
Since width can't be negative so, we take width = 10 inches
And height is given by
[tex]2x-6=2\times10-6=20-6=14\ in[/tex]
Hence, width will be 10 inches
and height will be 14 inches.
