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please help in 10th grade

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4.<AB is right angle. BX bisects < ABC. Find x if m<ABX= 2x-3?

5. Tell whether the lengths 8, 14, and 10 form the sides of an acute, right, obtuse, or not a triangle?

6. In the triangle, LJ= 9 and m<L= 40 find LR.

7. The legs of a triangle are 4 and 7, what is the length of the hypotenuse?
asked Feb 2, 2013 in GEOMETRY by anonymous Apprentice

2 Answers

+1 vote

5). The lengths 8, 14, and 10.

Check by using Pythagorean theorem.

If c2 = a2 + b2, then it is a right angle.

If c2 < a2 + b2, then it is a acute angle.

If c2 > a2 + b2, then it is a obtuse angle.

Here a = 8, b = 10, and c = 14

a2 = 82 = 64, b2 = 102 = 100, and c2 = 142 = 196.

By checking a2 + b2 = 64 + 100 = 164, c2 = 142 = 196.

a2 + b2 < c2 so, it is a obtuse angle.

answered Feb 2, 2013 by richardson Scholar
+1 vote

7). The legs of a triangle are 4 and 7.

Pythagoras' Theorem tells us:

The square of the hypotenuse is equal to the sum of the squares of the two shorter sides.

The hypotenuse is h2 = 42 + 72

h2 = 16 + 49 = 65

Apply square root each side.

h = √65 = 8.062.

answered Feb 3, 2013 by richardson Scholar

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