Mathematics po pasagot po

Answer:

1. $150cm^{2}$

2. 29cm

3. ∠B = ∠D = 99°, ∠A = ∠C = 81°

4. x = 6cm, y = 4cm, DF = 20cm, EG = 16cm

Step-by-step explanation:

1. $A=\frac{d_{1}d_{2}}{2} =\frac{15(20)}{2} =150cm^{2}$

2. $A=\frac{d_{1}d_{2}}{2}$

$d_{2}=\frac{2A}{d_{1}}=\frac{2(348)}{24} =29cm$

3. In a parallelogram, opposite angles are congruent; hence, ∠B = ∠D.

$4x+15=6x-27$

$2x=15+27$

$x=21$

∠B = 4(21) + 15 = 99°

∠D = 6(21) – 27 = 99°

Also, consecutive angles are supplementary (their sum is equal to 180).

∠A + ∠B = 180

∠A = 180 – 99 = 81°

∠C = ∠A = 81°

4. In a parallelogram, diagonals bisect each other.

$x+y=10$ (Eq. 1)

$2x-y=8$ (Eq. 2)

Solve for x using either substitution or elimination. The variable y can be eliminated by adding the two equations.

$3x=18$

$x=6$

$y=10-x=4$

After determining the values of x and y, find the length of DC and CG.

$DC=x+y=6+4=10cm$

$CG=2x-y=2(6)-4=8cm$

(Actually, there is no need to solve for DC and CG because it is equal to CF and CE, respectively.)

The lengths of the diagonals are

$DF=10+10=20cm$

$EG=8+8=16cm$

Mathematics po pasagot po​