Question

the perimeter of a window shaped as an isosceles triangle is 78 inches, if the base is 7 inches longer than either of the other two sides, how long is the base? you do not need to include the unit measurement or unit type. only the numerical answer is necessary. round to the nearest tenth if necessary.

Explanation:

Step1: Define variables

Let the length of each of the equal sides be \(x\) inches. Then the base length is \(x + 7\) inches.

Step2: Set up perimeter equation

The perimeter \(P\) of a triangle is \(P=\text{side}_1+\text{side}_2+\text{base}\). For an isosceles triangle with perimeter \(P = 78\) inches, we have \(x+x+(x + 7)=78\).
Simplify the left - hand side: \(3x+7 = 78\).

Step3: Solve for \(x\)

Subtract \(7\) from both sides: \(3x=78 - 7=71\).
Divide both sides by \(3\): \(x=\frac{71}{3}\approx23.7\).

Step4: Find the base length

The base length is \(x + 7\). Substitute \(x=\frac{71}{3}\) into \(x + 7\): \(\frac{71}{3}+7=\frac{71+21}{3}=\frac{92}{3}\approx30.7\).

Answer:

\(30.7\)