» Find the measure of a diagonal of the rectangle whose length and width are 12 and 9 respectively.
Think:
» If a rectangle was cut by its diagonal, it forms two congruent RightTriangles. Considering the length is congruent to the longer leg, the width is congruent to the shorter leg, and the diagonal is congruent to the hypothenuse.
length≅longerleg
width≅shorterleg
diagonal≅hypotenuse
Conduct a Formula:
» Since we are finding the side/s of a right triangle, we are using the PythagoreanTheorem: In which the sum of each square of the legs is the square of the hypotenuse.
a²+b²=c²
Solve:
» Substitute the given to find the hypotenuse (diagonal):
12² + 9² = c²
144 + 81 = c²
225 = c²
c = 15
Final Answer:
» The diagonal of a rectangle with the length of 12 and the width of 9 is 15.
Answers & Comments
Verified answer
RECT/RIGHT ANGLE
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Problem:
» Find the measure of a diagonal of the rectangle whose length and width are 12 and 9 respectively.
Think:
» If a rectangle was cut by its diagonal, it forms two congruent Right Triangles. Considering the length is congruent to the longer leg, the width is congruent to the shorter leg, and the diagonal is congruent to the hypothenuse.
Conduct a Formula:
» Since we are finding the side/s of a right triangle, we are using the Pythagorean Theorem: In which the sum of each square of the legs is the square of the hypotenuse.
Solve:
» Substitute the given to find the hypotenuse (diagonal):
Final Answer:
» The diagonal of a rectangle with the length of 12 and the width of 9 is 15.
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