A) Find KM∠KEM is a right angle hence ΔKEM is a right angled triangle Using Pythogoras' theorem where the square of hypotenuse is equal to the sum of the squares of the adjacent sides we can answer the
KM² = KE² + ME²KM² = 8² + (3√5)² = 64 + 9x5KM = √109KM = 10.44
b)Find LMThe ratio of LM:KN is 3:5 hence if we take the length of one unit as xlength of LM is 3xand the length of KN is 5x ∠K and ∠N are equal making it a isosceles trapezoid. A line from L that cuts KN perpendicularly at D makes KE = DN
KN = LM + 2x 2x = KE + DN2x = 8+8x = 8LM = 3x = 3*8 = 24
c)Find KN Since ∠K and ∠N are equal, when we take the 2 triangles KEM and LDN, they both have the same height ME = LD.
∠K = ∠N Hence KE = DN the distance ED = LMhence KN = KE + ED + DN since ED = LM = 24and KE + DN = 16KN = 16 + 24 = 40
d)Find area KLMNArea of trapezium can be calculated using the formula below Area = 1/2 x perpendicular height between parallel lines x (sum of the parallel sides)substituting values into the general equationArea = 1/2 * ME * (KN+ LM) = 1/2 * 3√5 * (40 + 24) = 1/2 * 3√5 * 64 = 3 x 2.23 * 32 = 214.66 units²
RU is a diameter, so the two equations make half a circle which is 180 degrees.
24x+5 + 10x+5 = 180
Combine like terms:
34x + 10 = 180
Subtract 10 from both sides:
34x = 170
Divide both sides by 34
X= 5
RS= UV
RS = 10x +5
Replace x with 5
RS = 10(5) + 5 = 55
Answers:
X = 5
RS = 55
Answer:
x = 20
Step-by-step explanation:
angle m<3 + angle m<5 = 180° because these angles are supplementary
5x + 10 + 3x + 10 = 180° add like terms
8x + 20 = 180
8x = 160 divide both sides by 8
x = 20
12 have a nice day plz mark as brainliest
