Answer:
Δ PQT ~ Δ QRS .....{S-S-S test for similarity}...Proof is below.
Step-by-step explanation:
Given:
In Δ PQT
PQ = 30 ft
QT = 28 ft
TP = 20 ft
In Δ QRS
QR = 15 ft
RS = 14 ft
SQ = 10 ft
To Prove:
Δ PQT ~ Δ QRS
Proof:
First we consider the ratio of the sides
..............( 1 )
..............( 2 )
..............( 3 )
So By equation ( 1 ), ( 2 ) and ( 3 ) we get
Now in Δ PQT and Δ QRS we have
Which are corresponding sides of a similar triangle in proportion.
∴ Δ PQT ~ Δ QRS .....{S-S-S test for similarity}...Proved
It takes 15 minutes for Ms. Peter to drive from park to her home
Given :
from her home to the park at an average speed of 30 miles per hour and
returned home along the same route at an average speed of 40 miles per hour
it takes 20 minutes to travel
Convert 20 minutes in to hour (divide by 60)
20 minutes = 1/3 hour
We know that distance = speed x time
From home to park, distance =
So , distance between home and park is 10 miles
Now we calculate the time taken to return from park to home
Time taken is 1/4 hours. Convert it into minutes by multiplying by 60
So it takes 15 minutes for Ms. Peter to drive from park to her home
Learn more : brainly.com/question/18839247
Answer: ∠ J = 62° , ∠ K = 59° , ∠ L = 59°
<u>Step-by-step explanation:</u>
It is given that it is an Isosceles Triangle, where L J ≅ K J
It follows that ∠ K ≅ ∠ L
⇒ 5x + 24 = 4x + 31
⇒ x + 24 = 31
⇒ x = 7
Input the x-value into either equation to solve for ∠ K & ∠ L:
∠ K = 5x + 24
= 5(7) + 24
= 35 + 24
= 59
∠ K ≅ ∠ L ⇒ ∠ L = 59
Next, find the value of ∠ J:
∠ J + ∠ K + ∠ L = 180 Triangle Sum Theorem
∠ J + 59 + 59 = 180
∠ J + 118 = 180
∠ J = 62
Answer:
183 miles to the nearest mile.
Step-by-step explanation:
Distance =Speed X Time
Distance of Truck B from point A=45 X2 =90 miles
Distance of Truck C from point A=55 X2 =110 miles
Angles between them, BAC=132°
We want to find the Distance BC denoted by a between the trucks.
Using Cosine Rule,
a²=b²+c²-2bcCos A
=90²+110²-(2X90X110XCos132°)
=33448.79
a=√33448.79
BC=182.89 miles
The distance between the trucks is 183 miles to the nearest mile.
You can solve this by doing 8×8×6 which gives you 384. Since we are finding the volume, you would do length times with times height. Hope this helps :-)
