Answer:
To solve this problem, we can use the Pythagorean theorem, which relates the sides of a right triangle. Let's call the height "h" and the width "w". Then we have: w = h + 7 (since the width is 7 inches longer than the height) We also know that the diagonal measurement is 34 inches, so we can use the Pythagorean theorem to relate the height, width, and diagonal: h^2 + w^2 = d^2 Substituting the values we have: h^2 + (h+7)^2 = 34^2 Expanding and simplifying: 2h^2 + 14h - 795 = 0 Now we can solve for h using the quadratic formula: h = (-14 ± sqrt(14^2 - 4(2)(-795))) / (