Question

what is the missing length?
image of a triangle with height 38 in (dashed line with right angle), base labeled t
area = 1159 in²
t = ____ inches
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Explanation:

Step1: Recall the area formula for a triangle

The area \( A \) of a triangle is given by \( A=\frac{1}{2}\times\text{base}\times\text{height} \). Here, the height \( h = 38 \) in and the area \( A=1159 \) \( \text{in}^2 \), and the base is \( t \). So we have the formula \( 1159=\frac{1}{2}\times t\times38 \).

Step2: Simplify the right - hand side of the equation

First, simplify \( \frac{1}{2}\times38 \). \( \frac{1}{2}\times38 = 19 \). So the equation becomes \( 1159 = 19t \).

Step3: Solve for \( t \)

To find \( t \), we divide both sides of the equation \( 1159 = 19t \) by 19. So \( t=\frac{1159}{19} \). Calculating \( \frac{1159}{19}=61 \).

Answer:

61