Given rectangle MATH. What is the measure of overline MT . if overline MH = 5cm and overline AH = 9cm ?
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Given rectangle MATH. What is the measure of overline MT . if overline MH = 5cm and overline AH = 9cm ?
Given rectangle MATH. What is the measure of overline MT . if overline MH = 5cm and overline AH = 9cm ?
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Answer:
Assuming that point H is on side MA, we can use the Pythagorean theorem to find the length of side AT. The theorem states that in a right triangle, the sum of the squares of the two shorter sides (the legs) is equal to the square of the longest side (the hypotenuse). In this case, we have a right triangle with legs MH and AH and hypotenuse MA, so we can write:
MA^2 = MH^2 + AH^2
Plugging in the given values, we get:
MA^2 = 5^2 + 9^2 MA^2 = 106 MA = sqrt(106)
Now, we can use the fact that opposite sides of a rectangle are equal in length to find the length of side MT. That is, we know that MA = TH, so:
MT = MA - AH
Substituting the values we have found, we get:
MT = sqrt(106) - 9
This is the measure of overline MT in terms of square roots. If you want a numerical approximation, you can use a calculator to find:
MT ≈ 0.934 cm