Question

Please show your work!!!

PLEASE DONT TYPE RANDOM THINGS PLEASE!!!

Answer 1

Answer:

Using angle sum property of a triangle in ∆ABC:

∠A + ∠B + ∠C = 180º

=> ∠A + 64º + 49º = 180º

=> ∠A = 67º

Now, given that ∆ABC ~ ∆PQR:

∠A = ∠P = 67º

∠B = ∠Q = 64º

∠C = ∠R = 49º

(using AAA criterion of similarity)

The ratio of corresponding sides is equal if two triangles are similar. Using this:

$\frac{AB}{PQ} = \frac{BC}{QR} = \frac{AC}{PR}$

Now,

$\frac{AB}{PQ} = \frac{BC}{QR}$

=> $\frac{AB}{19} = \frac{46}{23}$

=> AB = 38 in

Similarly,

$\frac{BC}{QR} = \frac{AC}{PR}$

=> $\frac{46}{23} = \frac{AC}{22.5}$

=> AC = 45 in

Now, perimeter of ∆ABC:

AB + BC + AC = 38 + 46 + 45 = 129 in

Given that parallelogram ABCD ~ parallelogram JKLM

=> ∠A = ∠J (corresponding angles are equal in similar parallelograms)

and ∠A = ∠C (opposite angles are equal in a parallelogram)

Now, ∠A = ∠C = ∠J = 120º

The ratio of corresponding sides is equal if two parallelograms are similar. Using this:

$\frac{AB}{JK} = \frac{BC}{KL} = \frac{CD}{LM} = \frac{AD}{JM}$

Now,

$\frac{BC}{KL} = \frac{CD}{LM}$

We also know that BC = AD = 7 ft and AB = CD = 9 ft (opposite sides of a parallelogram are equal)

=> $\frac{7}{3.5} = \frac{9}{LM}$

=> LM = 4.5 ft