Δ MAL and Δ DLA are right triangles. If Δ MAL ≅ ΔDLA, then side DL is congruent to side MA, and ∠ MAL is congruent to ∠ DLA. Given ∠ M is 30 °, side DL is (2x + 10) cm, side MA is (3x – 2) cm, and side AL is (x + 5) cm, answer the following questions below: What is the measurement of DL?

What is the measurement of AL?

What is the measurement of ∠ DLA?

What is the measurement of ∠ AEL?

DL = 34 cm

AL = 17 cm

∠DLA = 60°

∠ADL = 30°

Step-by-step explanation:

Given:

   DL ≅ MA

⇒ 2x + 10 = 3x - 2

⇒ 2x + 12 = 3x

⇒ 12 = x

Substituting found value of x into expressions for DL and AL:

DL = 2x + 10

     = 2(12) + 10

     = 34 cm

AL = x + 5

    = 12 + 5

    = 17 cm

The only way for ΔMAL to be a right triangle, with MA = 34 cm, AL = 17 cm and ∠M = 30° is if

Given:

Sum of interior angles of a triangle is 180°

⇒ ∠DLA + 30° + 90° = 180°

⇒ ∠DLA + 120° = 180°

⇒ ∠DLA = 60°

As ∠M = ∠D = 30°, then ∠ADL = 30°

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

Cost of 7 gallons=$24.50

Cost of 1 gallon=24.50/7=3.5

Cost of 15 gallons=15*3.5=52.5

Cost of 15 gallons will be $52.5

The answer is in the image 

For every 8 cars there are 7 trucks

Therefore,

Cars:Truck=8:7

Answer is B)8:7

The solution is in the following image

The answer is in the image 

The answer is in the image 

Speed=Distance/time

Here,

distance=15m

time=1sec

speed=15/1=15m/sec

Distance=Speed*time

time=15min=15*60sec=900sec

Distance travelled in 15 min=15*900=13,500m

=13500/1000 km=13.5Km

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.