Answer:
[tex]150\ in^2[/tex]
Step-by-step explanation:
Given triangle is right triangle. Use the Pythagorean theorem to find the second leg:
[tex]25^2=15^2+x^2,\\ \\625=225+x^2,\\ \\x^2=625-225,\\ \\x^2=400,\\ \\x=20\ in.[/tex]
Then use formula for the right triangle's area
[tex]A=\dfrac{1}{2}\cdot \text{leg}_1\cdot \text{leg}_2.[/tex]
Thus,
[tex]A=\dfrac{1}{2}\cdot 15\cdot 20=150\ in^2.[/tex]
