Question

One mirror is to be in the shape of a triangle whose height is 6 feet less than twice the base of the mirror. If the mirror has an area of 108 sqaure feet, what are the base and height of the mirror?

Answer 1

Answer:

Base of the mirror is 12 feet and height of the mirror is 18 feet.

Step-by-step explanation:

Given:

Area of the triangular mirror = 108 sq ft.

Let base (b) of the mirror be x.

Now given:

height is 6 feet less than twice the base of the mirror

So we can say that;

Height (h) = $2x-6$

We need to find the base and height of the mirror.

Solution:

Now we know that mirror is in triangular shape so we will apply area of triangle formula to find base and height.

Now Area of triangle is half times base times height.

framing in equation form we get;

$108=\frac{1}{2} \times x \times(2x-6)\\\\108=\frac{1}{2}\times x \times 2(x-3)\\\\108=x(x-3)\\\\108=x^2-3x\\\\x^2-3x-108=0$

Now we will find the roots of x by factorizing the equation we get;

$x^2-12x+9x-108=0\\\\x(x-12)+9(x-12)=0\\\\(x-12)(x+9)=0$

Now we will solve for 2 values of x we get;

$x-12=0\\\\x=12\ ft\\\\Also;\\\\x+9=0\\\\x=-9\ ft$

Now we get 2 values of 'x' one positive and one negative.

Since x is base of the triangle which cannot be negative.

so we will discard the negative value.

Hence;

base of triangle = 12 ft

Height of the triangle = $2x-6=2\times12-6 =24-6 =18\ ft$

Hence Base of the mirror is 12 feet and height of the mirror is 18 feet.