Question

The ratio of the lengths of the two legs of a right triangle is 3:4

(a) Find the length of each leg when the length of the hypotenuse
is the given measure. (b) Find the area of the triangle.
d. 100 cm
a. 10 cm
b. 20 cm
c. 25 cm

Answer 1

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Check Attachment!!!

According to the statement of the question, we have:

a/b = 3/4

Note that according to the attached figure, b > a, then the correct proportion will be a to 3, as well as b to 4, because b > a and 4 > 3

Isolating a and b:

a = 3b/4

b = 4a/3

From Pythagoras:

h² = a² + b² - as a = 3b/4 and b = 4a/3, so

b = 4h/5

a = 6h/5

For Area:

A = b.a/2

as b = 4h/5 and a = 6h/5, so

A = 12h/25