Given triangle JKL is congruent to triangle PQR. Find x and RP x= RP=

Mathematics

1 answer:

sergejj [24]2 years ago

6 0

Answer:

RP=15

x=14

Step-by-step explanation:

ΔJKL≅ΔPQR so JK=PQ, KL=QR, and JL=PR.

KL=3y-2 and QR=22

So, 3y-2=22 and 3y=24 and y=8

Now, that we know y=8 we can plug it in 2y-1 to find RP

2(8)-1=16-1=15

In congruent triangles, the corresponding angles are also congruent.

So, ∠K≅∠Q

∠K=42 and ∠Q=3x

So, 42=3x and x=14

You might be interested in

Find the missing side lengths leave your answer as a racials simplest form

Aleksandr-060686 [28]

Answer:

m= $7\sqrt3$

n=7

Step-by-step explanation:

Hi there!

We are given a right triangle (notice the 90°) angle, the measure of one of the acute angles as 60°, and the measure of the hypotenuse (the side OPPOSITE from the 90 degree angle) as 14

We need to find the lengths of m and n

Firstly, let's find the measure of the other acute angle

The acute angles in a right triangle are complementary, meaning they add up to 90 degrees

Let's make the measure of the unknown acute angle x

So x+60°=90°

Subtract 60 from both sides

x=30°

So the measure of the other acute angle is 30 degrees

This makes the right triangle a special kind of right triangle, a 30°-60°-90° triangle

In a 30°-60°-90° triangle, if the length of the hypotenuse is a, then the length of the leg (the side that makes up the right angle) opposite from the 30 degree angle is $\frac{a}{2}$ , and the leg opposite from the 60 degree angle is $\frac{a\sqrt3}{2}$